$9$ . Simone is designing a piece of artwork in the shape of a square pyramid for a hotel. She wants to cover the pyramid with decorative glass. How many square feet of glass does Simone need to cover the entire pyramid?

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. Simone is designing a piece of artwork in the shape of a square pyramid for a hotel. She wants to cover the pyramid with decorative glass. How many square feet of glass does Simone need to cover the entire pyramid?

Define Base and Slant Height: To find the total area of glass needed, we need to know the area of the base and the area of the four triangular faces of the pyramid. Let's assume the side length of the base is $s$ and the slant height is $l$ .
Calculate Base Area: First, calculate the area of the base, which is a square. The formula for the area of a square is side length squared, so it's $s^2$ .
Calculate Triangle Area: Next, calculate the area of one triangular face using the formula $(\text{base} \times \text{slant height}) / 2$ . Since the base of each triangle is $'s'$ and the slant height is $'l'$ , the area of one triangle is $(s \times l) / 2$ .
Calculate Total Triangle Area: Since there are four identical triangular faces, multiply the area of one triangle by $4$ to get the total area of the four triangles. So, it's $4 \times (s \times l) / 2$ .
Calculate Total Surface Area: Now, add the area of the base to the total area of the four triangles to get the total surface area of the pyramid. So, the total area is $s^2 + 4 \times (s \times l) / 2$ .
Need Actual Measurements: Let's plug in the numbers. Oops, we don't have the actual measurements for ' $s$ ' and ' $l$ '. We need those to calculate the exact area. Without them, we can't solve the problem.